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Intersection 30

Intersection 30
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2016-04-03 07:38
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to find the intersection of two lines using geometric construction methods. Key mathematical concepts include linear equations and vectors. Using GeoGebra commands such as Line, Intersect, Mirror, etc., the geometric meaning of the intersection point can be intuitively understood. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. AngularBisector(B, C, A) → f
  3. AngularBisector(C, A, B) → d
  4. AngularBisector(A, B, C) → e
  5. Intersect(d, e) → D
  6. AngularBisector(C, A, D) → g
  7. AngularBisector(D, C, A) → h
  8. Intersect(g, h) → E
  9. AngularBisector(D, A, B) → j
  10. AngularBisector(D, B, A) → l
  11. Intersect(j, l) → G
  12. Segment(E, G) → t
  13. Mirror(d, t) → d'
  14. AngularBisector(B, C, D) → n
  15. AngularBisector(D, B, C) → q
  16. Intersect(n, q) → I
  17. Segment(I, G) → b_1
  18. Mirror(e, b_1) → e'
  19. Intersect(d', e') → O
  20. Line(B, C) → b
  21. OrthogonalLine(I, b) → r
  22. Intersect(b, r) → J
  23. AngularBisector(O, J, C) → i_1
  24. Intersect(i_1, f) → T
  25. OrthogonalLine(T, b) → j_1
  26. Intersect(b, j_1) → U
  27. Circle(T, U) → p_1
  28. AngularBisector(O, J, B) → g_1
  29. Intersect(e, g_1) → R
  30. OrthogonalLine(R, a) → h_1
  31. Intersect(a, h_1) → S
  32. Circle(R, S) → k_1
  33. Intersect(p_1, k_1) → V, , ,
  34. OrthogonalLine(V, b) → l_1
  35. Intersect(b, l_1) → W
  36. Midpoint(V, W) → B_1
  37. Circle(V, W) → q_1
  38. Intersect(k_1, q_1) → Z, A_1, ,
  39. Line(A_1, Z) → m_1
  40. Line(B_1, m_1) → n_1
  41. Dilate(q_1, 0.5, W) → r_1
  42. Intersect(r_1, n_1) → C_1, D_1
  43. Mirror(r_1, D_1) → s_1
  44. Mirror(s_1, q_1) → t_1
  45. Intersect(t_1, b) → D_2,
  46. Line(C, A) → c
  47. OrthogonalLine(E, c) → i
  48. Intersect(c, i) → F
  49. AngularBisector(O, F, A) → c_1
  50. Intersect(d, c_1) → P
  51. OrthogonalLine(P, a) → e_1
  52. Intersect(a, e_1) → Q
  53. Circle(P, Q) → f_1
  54. Intersect(f_1, k_1, 1) → L_1
  55. OrthogonalLine(L_1, a) → h_2
  56. Intersect(a, h_2) → M_1
  57. Circle(L_1, M_1) → k_2
  58. Intersect(k_2, f_1) → O_1, P_1, ,
  59. Line(P_1, O_1) → i_2
  60. Midpoint(M_1, L_1) → N_1
  61. Line(N_1, i_2) → j_2
  62. Circle(N_1, M_1) → p_2
  63. Intersect(p_2, j_2) → Q_1, R_1
  64. Mirror(p_2, Q_1) → q_2
  65. Mirror(q_2, k_2) → r_2
  66. Intersect(r_2, a) → B_2,
  67. Circle(E, F) → k
  68. OrthogonalLine(G, a) → m
  69. Intersect(a, m) → H
  70. Circle(G, H) → p
  71. Circle(I, J) → s
  72. Intersect(k, d) → K, N
  73. Intersect(p, d) → L, M
  74. Segment(E, I) → a_1
  75. Mirror(f, a_1) → f'
  76. AngularBisector(A, H, O) → d_1
  77. Intersect(f_1, p_1, 1) → E_1
  78. OrthogonalLine(E_1, c) → a_2
  79. Intersect(c, a_2) → F_1
  80. Midpoint(F_1, E_1) → G_1
  81. Circle(G_1, F_1) → c_2
  82. Circle(E_1, F_1) → d_2
  83. Intersect(f_1, d_2) → H_1, I_1, ,
  84. Line(I_1, H_1) → b_2
  85. Line(G_1, b_2) → e_2
  86. Intersect(c_2, e_2) → J_1, K_1
  87. Mirror(c_2, J_1) → f_2
  88. Mirror(f_2, d_2) → g_2
  89. Center(f_1) → S_1
  90. Center(p_1) → T_1
  91. Center(k_1) → U_1
  92. Center(r_2) → V_1
  93. Center(g_2) → W_1
  94. Center(t_1) → Z_1
  95. Segment(C, B_2) → m_2
  96. Segment(D_2, A) → l_2
  97. Intersect(l_2, m_2) → A_2
  98. Intersect(g_2, c) → C_2,
  99. Segment(C_2, B) → n_2